What problems must be handled if the ISS would be dismounted and carried to the Moon piece by piece and landed there? What preparations would be required for such an installation since the ISS's components aren't designed for being installed on any surface?

You would obviously need VERY large cargo vehicle to land with some of the big pieces. And LOTS of fuel to get them there. And as you say, the station is designed for zero gravity, so all kinds of things, like the solar panel unfurling and aiming mechanism would not work at all. In fact, I doubt all the parts would even have the structural strength to stay assembled in 1/6 G. It would probably collapse into a pile of broken parts on the surface, like a jellyfish out of water.

There is a definite 'up' and 'down' designed into the ISS, but windows are in the 'floor' so that the crew can look at the Earth.

A more reasonable 'second life' for the ISS might be as a cycling space station in the 2:1 resonant orbit proposed by Heppenheimer. Trips to the moon would then be like a sea cruise, rather than crossing the Atlantic in the Spirit of St Louis.

I suspect that in practice, by the time there is a need for such a thing, the ISS will be completely knackered.

A more reasonable 'second life' for the ISS might be as a cycling space station in the 2:1 resonant orbit proposed by Heppenheimer. ... I suspect that in practice, by the time there is a need for such a thing, the ISS will be completely knackered.

I agree completely.

Frediiiie, I agree the panels cannot stand gravity, but astronauts COULD just lay them on the ground, very carefully and by hand. Still, ISS would need a LOT more batteries to last through a 2 week night.

So really the only useful thing is the habitable volume, and that could be supplied much more easily by some Bigelow modules. It probably will be.